Border Padding

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• Author: Diego Inácio
• GitHub: github.com/diegoinacio
• Notebook: border_padding.ipynb

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Bi-dimensional image padding for spatial filtering and convolution.

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from numba import stencil
import imageio

from _utils import *

import warnings
warnings.filterwarnings('ignore')

0. Input image and Box Filter function

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img_in = imageio.imread('../_data/fruits.png')

histogram(img_in, bins=2**8)

def pbox_filter(M, r):
    @stencil(neighborhood=(
        (-r, r),
        (-r, r)
    ))
    def box_filter(M):
        output = 0
        for i in range(-r, r + 1):
            for j in range(-r, r + 1):
                output += M[i, j]
        return output/(2*r + 1)**2
    return box_filter(M)

def pbox_filterRGB(img, r):
    img_out = img.copy()
    img_out[..., 0] = pbox_filter(img[..., 0], r)
    img_out[..., 1] = pbox_filter(img[..., 1], r)
    img_out[..., 2] = pbox_filter(img[..., 2], r)
    return img_out

dict_panel = {
    'text_color': 'red',
    'text_size': 20,
    'texts': ['Input image', 'Filtered image']
}
img_f0 = pbox_filterRGB(img_in , 35)
panel(
    np.array([img_in, img_f0]),
    gspec=(2, 1), **dict_panel
)

Without padding, the border of the filtered image will receive 0.

1. Zero Padding

---

Pads with a constant value (0 in this case), resulting in a artifact with the same value on the border.

|A B C D E F|

0 0 0 |A B C D E F| 0 0 0

# Filter radius
r = 35

img_pad1 = np.pad(
    img_in,
    ((r, r), (r, r), (0, 0)),
    'constant',
    constant_values=0
)

histogram(img_pad1)

img_f1 = pbox_filterRGB(img_pad1 , r)[r:-r, r:-r]
panel(
    np.array([img_in, img_f1]),
    gspec=(2, 1), **dict_panel
)

We can notice a black border on the filtered image.

2. Wrap Padding

---

Pads with a modular repetition of each axis, resulting in some artifacts from the opposite edges.

|A B C D E F|

D E F |A B C D E F| A B C

img_pad2 = np.pad(
    img_in,
    ((r, r), (r, r), (0, 0)),
    'wrap'
)

histogram(img_pad2)

img_f2 = pbox_filterRGB(img_pad2 , r)[r:-r, r:-r]
panel(
    np.array([img_in, img_f2]),
    gspec=(2, 1), **dict_panel
)

We can notice a red artifact on the top of the filtered image which was spread from the bottom part.

3. Reflect Padding

---

Pads with the reflection of each axis.

|A B C D E F|

D C B |A B C D E F| E D C

img_pad3 = np.pad(
    img_in,
    ((r, r), (r, r), (0, 0)),
    'reflect'
)

histogram(img_pad3)

img_f3 = pbox_filterRGB(img_pad3 , r)[r:-r, r:-r]
panel(
    np.array([img_in, img_f3]),
    gspec=(2, 1), **dict_panel
)

4. Edge Padding

---

Pads with the edge pixel of each axis.

|A B C D E F|

A A A |A B C D E F| F F F

img_pad4 = np.pad(
    img_in,
    ((r, r), (r, r), (0, 0)),
    'edge'
)

histogram(img_pad4)

img_f4 = pbox_filterRGB(img_pad4 , r)[r:-r, r:-r]
panel(
    np.array([img_in, img_f4]),
    gspec=(2, 1), **dict_panel
)